I was thinking of booking a flight that leaves at 6.15am in the morning from MEX, which means that I'll have to get there at 4.15am or so. What are my options for getting there so early in the morning, since I read that the metros run beginning at 5am?
Since you haven't told us where you are, I'll assume you're somewhere else within or near by Mexico City. Your best bet will be a taxi.
Public transport (buses and trains) don't start until 4:30am or later: